|x-3|>2x+1

Solution

∣ x - 3 ∣ > 2 x + 1

x < \frac{2}{3}

Interval Notation

(- \infty, \frac{2}{3})

Decimal Notation

x < 0.66666 \dots

Solution steps

∣ x - 3 ∣ > 2 x + 1

Find positive and negative intervals

x < 3, x \geq 3

Solve the inequality for each interval

x < \frac{2}{3} or No Solution

Merge Overlapping Intervals

x < \frac{2}{3}

∣ 2 x - 4 ∣ < x - 1

x^{2} - x - 2 > 2

∣ 5 - x ∣ + ∣ x - 13 ∣ < ∣ 2 - x ∣

∣ x ∣ + ∣ x - 4 ∣ > 4

(b) ∣ x + 2 ∣ + 2 \geq 0